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Model Assisted Survey Sampling


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Table of Contents

I Principles of Estimation for Finite Populations and Important Sampling Designs.- 1 Survey Sampling in Theory and Practice.- 1.1 Surveys in Society.- 1.2 Skeleton Outline of a Survey.- 1.3 Probability Sampling.- 1.4 Sampling Frame.- 1.5 Area Frames and Similar Devices.- 1.6 Target Population and Frame Population.- 1.7 Survey Operations and Associated Sources of Error.- 1.8 Planning a Survey and the Need for Total Survey Design.- 1.9 Total Survey Design.- 1.10 The Role of Statistical Theory in Survey Sampling.- Exercises.- 2 Basic Ideas in Estimation from Probability Samples.- 2.1 Introduction.- 2.2 Population, Sample, and Sample Selection.- 2.3 Sampling Design.- 2.4 Inclusion Probabilities.- 2.5 The Notion of a Statistic.- 2.6 The Sample Membership Indicators.- 2.7 Estimators and Their Basic Statistical Properties.- 2.8 The ? Estimator and Its Properties.- 2.9 With-Replacement Sampling.- 2.10 The Design Effect.- 2.11 Confidence Intervals.- Exercises.- 3 Unbiased Estimation for Element Sampling Designs.- 3.1 Introduction.- 3.2 Bernoulli Sampling.- 3.3 Simple Random Sampling.- 3.3.1 Simple Random Sampling without Replacement.- 3.3.2 Simple Random Sampling with Replacement.- 3.4 Systematic Sampling.- 3.4.1 Definitions and Main Result.- 3.4.2 Controlling the Sample Size.- 3.4.3 The Efficiency of Systematic Sampling.- 3.4.4 Estimating the Variance.- 3.5 Poisson Sampling.- 3.6 Probability Proportional-to-Size Sampling.- 3.6.1 Introduction.- 3.6.2 ?ps Sampling.- 3.6.3 pps Sampling.- 3.6.4 Selection from Randomly Formed Groups.- 3.7 Stratified Sampling.- 3.7.1 Introduction.- 3.7.2 Notation, Definitions, and Estimation.- 3.7.3 Optimum Sample Allocation.- 3.7.4 Alternative Allocations under STSI Sampling.- 3.8 Sampling without Replacement versus Sampling with Replacement.- 3.8.1 Alternative Estimators for Simple Random Sampling with Replacement.- 3.8.2 The Design Effect of Simple Random Sampling with Replacement.- Exercises.- 4 Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages.- 4.1 Introduction.- 4.2 Single-Stage Cluster Sampling.- 4.2.1 Introduction.- 4.2.2 Simple Random Cluster Sampling.- 4.3 Two-Stage Sampling.- 4.3.1 Introduction.- 4.3.2 Two-Stage Element Sampling.- 4.4 Multistage Sampling.- 4.4.1 Introduction and a General Result.- 4.4.2 Three-Stage Element Sampling.- 4.5 With-Replacement Sampling of PSUs.- 4.6 Comparing Simplified Variance Estimators in Multistage Sampling.- Exercises.- 5 Introduction to More Complex Estimation Problems.- 5.1 Introduction.- 5.2 The Effect of Bias on Confidence Statements.- 5.3 Consistency and Asymptotic Unbiasedness.- 5.4 ? Estimators for Several Variables of Study.- 5.5 The Taylor Linearization Technique for Variance Estimation.- 5.6 Estimation of a Ratio.- 5.7 Estimation of a Population Mean.- 5.8 Estimation of a Domain Mean.- 5.9 Estimation of Variances and Covariances in a Finite Population.- 5.10 Estimation of Regression Coefficients.- 5.10.1 The Parameters of Interest.- 5.10.2 Estimation of the Regression Coefficients.- 5.11 Estimation of a Population Median.- 5.12 Demonstration of Result 5.10.1.- Exercises.- II Estimation through Linear Modeling, Using Auxiliary Variables.- 6 The Regression Estimator.- 6.1 Introduction.- 6.2 Auxiliary Variables.- 6.3 The Difference Estimator.- 6.4 Introducing the Regression Estimator.- 6.5 Alternative Expressions for the Regression Estimator.- 6.6 The Variance of the Regression Estimator.- 6.7 Comments on the Role of the Model.- 6.8 Optimal Coefficients for the Difference Estimator.- Exercises.- 7 Regression Estimators for Element Sampling Designs.- 7.1 Introduction.- 7.2 Preliminary Considerations.- 7.3 The Common Ratio Model and the Ratio Estimator.- 7.3.1 The Ratio Estimator under SI Sampling.- 7.3.2 The Ratio Estimator under Other Designs.- 7.3.3 Optimal Sampling Design for the ? Weighted Ratio Estimator.- 7.3.4 Alternative Ratio Models.- 7.4 The Common Mean Model.- 7.5 Models Involving Population Groups.- 7.6 The Group Mean Model and the Poststratified Estimator.- 7.7 The Group Ratio Model and the Separate Ratio Estimator.- 7.8 Simple Regression Models and Simple Regression Estimators.- 7.9 Estimators Based on Multiple Regression Models.- 7.9.1 Multiple Regression Models.- 7.9.2 Analysis of Variance Models.- 7.10 Conditional Confidence Intervals.- 7.10.1 Conditional Analysis for BE Sampling.- 7.10.2 Conditional Analysis for the Poststratification Estimator.- 7.11 Regression Estimators for Variable-Size Sampling Designs.- 7.12 A Class of Regression Estimators.- 7.13 Regression Estimation of a Ratio of Population Totals.- Exercises.- 8 Regression Estimators for Cluster Sampling and Two-Stage Sampling.- 8.1 Introduction.- 8.2 The Nature of the Auxiliary Information When Clusters of Elements Are Selected.- 8.3 Comments on Variance and Variance Estimation in Two-Stage Sampling.- 8.4 Regression Estimators Arising Out of Modeling at the Cluster Level.- 8.5 The Common Ratio Model for Cluster Totals.- 8.6 Estimation of the Population Mean When Clusters Are Sampled.- 8.7 Design Effects for Single-Stage Cluster Sampling.- 8.8 Stratified Clusters and Poststratified Clusters.- 8.9 Regression Estimators Arising Out of Modeling at the Element Level.- 8.10 Ratio Models for Elements.- 8.11 The Group Ratio Model for Elements.- 8.12 The Ratio Model Applied within a Single PSU.- Exercises.- III Further Questions in Design and Analysis of Surveys.- 9 Two-Phase Sampling.- 9.1 Introduction.- 9.2 Notation and Choice of Estimator.- 9.3 The ?* Estimator.- 9.4 Two-Phase Sampling for Stratification.- 9.5 Auxiliary Variables for Selection in Two Phases.- 9.6 Difference Estimators.- 9.7 Regression Estimators for Two-Phase Sampling.- 9.8 Stratified Bernoulli Sampling in Phase Two.- 9.9 Sampling on Two Occasions.- 9.9.1 Estimating the Current Total.- 9.9.2 Estimating the Previous Total.- 9.9.3 Estimating the Absolute Change and the Sum of the Totals.- Exercises.- 10 Estimation for Domains.- 10.1 Introduction.- 10.2 The Background for Domain Estimation.- 10.3 The Basic Estimation Methods for Domains.- 10.4 Conditioning on the Domain Sample Size.- 10.5 Regression Estimators for Domains.- 10.6 A Ratio Model for Each Domain.- 10.7 Group Models for Domains.- 10.8 Problems Arising for Small Domains; Synthetic Estimation.- 10.9 More on the Comparison of Two Domains.- Exercises.- 11 Variance Estimation.- 11.1 Introduction.- 11.2 A Simplified Variance Estimator under Sampling without Replacement.- 11.3 The Random Groups Technique.- 11.3.1 Independent Random Groups.- 11.3.2 Dependent Random Groups.- 11.4 Balanced Half-Samples.- 11.5 The Jackknife Technique.- 11.6 The Bootstrap.- 11.7 Concluding Remarks.- Exercises.- 12 Searching for Optimal Sampling Designs.- 12.1 Introduction.- 12.2 Model-Based Optimal Design for the General Regression Estimator.- 12.3 Model-Based Optimal Design for the Group Mean Model.- 12.4 Model-Based Stratified Sampling.- 12.5 Applications of Model-Based Stratification.- 12.6 Other Approaches to Efficient Stratification.- 12.7 Allocation Problems in Stratified Random Sampling.- 12.8 Allocation Problems in Two-Stage Sampling.- 12.8.1 The ? Estimator of the Population Total.- 12.8.2 Estimation of the Population Mean.- 12.9 Allocation in Two-Phase Sampling for Stratification.- 12.10 A Further Comment on Mathematical Programming.- 12.11 Sampling Design and Experimental Design.- Exercises.- 13 Further Statistical Techniques for Survey Data.- 13.1 Introduction.- 13.2 Finite Population Parameters in Multivariate Regression and Correlation Analysis.- 13.3 The Effect of Sampling Design on a Statistical Analysis.- 13.4 Variances and Estimated Variances for Complex Analyses.- 13.5 Analysis of Categorical Data for Finite Populations.- 13.5.1 Test of Homogeneity for Two Populations.- 13.5.2 Testing Homogeneity for More than Two Finite Populations.- 13.5.3 Discussion of Categorical Data Tests for Finite Populations.- 13.6 Types of Inference When a Finite Population Is Sampled.- Exercises.- IV A Broader View of Errors in Surveys.- 14 Nonsampling Errors and Extensions of Probability Sampling Theory.- 14.1 Introduction.- 14.2 Historic Notes: The Evolution ofthe Probability Sampling Approach.- 14.3 Measurable Sampling Designs.- 14.4 Some Nonprobability Sampling Methods.- 14.5 Model-Based Inference from Survey Samples.- 14.6 Imperfections in the Survey Operations.- 14.6.1 Ideal Conditions for the Probability Sampling Approach.- 14.6.2 Extension of the Probability Sampling Approach.- 14.7 Sampling Frames.- 14.7.1 Frame Imperfections.- 14.7.2 Estimation in the Presence of Frame Imperfections.- 14.7.3 Multiple Frames.- 14.7.4 Frame Construction and Maintenance.- 14.8 Measurement and Data Collection.- 14.9 Data Processing.- 14.10 Nonresponse.- Exercises.- 15 Nonresponse.- 15.1 Introduction.- 15.2 Characteristics of Nonresponse.- 15.2.1 Definition of Nonresponse.- 15.2.2 Response Sets.- 15.2.3 Lack of Unbiased Estimators.- 15.3 Measuring Nonresponse.- 15.4 Dealing with Nonresponse.- 15.4.1 Planning of the Survey.- 15.4.2 Callbacks and Follow-Ups.- 15.4.3 Subsampling of Nonrespondents.- 15.4.4 Randomized Response.- 15.5 Perspectives on Nonresponse.- 15.6 Estimation in the Presence of Unit Nonresponse.- 15.6.1 Response Modeling.- 15.6.2 A Useful Response Model.- 15.6.3 Estimators That Use Weighting Only.- 15.6.4 Estimators That Use Weighting as Well as Auxiliary Variables.- 15.7 Imputation.- Exercises.- 16 Measurement Errors.- 16.1 Introduction.- 16.2 On the Nature of Measurement Errors.- 16.3 The Simple Measurement Model.- 16.4 Decomposition of the Mean Square Error.- 16.5 The Risk of Underestimating the Total Variance.- 16.6 Repeated Measurements as a Tool in Variance Estimation.- 16.7 Measurement Models Taking Interviewer Effects into Account.- 16.8 Deterministic Assignment of Interviewers.- 16.9 Random Assignment of Interviewers to Groups.- 16.10 Interpenetrating Subsamples.- 16.11 A Measurement Model with Sample-Dependent Moments.- Exercises.- 17 Quality Declarations for Survey Data.- 17.1 Introduction.- 17.2 Policies Concerning Information on Data Quality.- 17.3 Statistics Canada's Policy on Informing Users of Data Quality and Methodology.- Exercise.- Appendix A Principles of Notation.- Appendix B The MU284 Population.- Appendix C The Clustered MU284 Population.- Appendix D The CO124 Population.- References.- Answers to Selected Exercises.- Author Index.

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"I would recommend that this book be in the office of every survey methodologist."
(Journal of Official Statistics)

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